Add a new page

Let's start talking about the procedure that you need to go through in order to find out what the best assets are in an increasing cost of funds environment.

What I've done here is created a graph that allows you to see the internal rate of return criteria with the tool that we'll eventually use for increasing rate of return. And what I've done here is arranged assets A, B, C, D, and E in a decreasing internal rate of return, so that the height of each one of these bars here represents actually the internal rate of return, while the width represents the initial investment you have to make — that's why this is [unintelligible] having an i for an interest rate, and this over here is the scale of investment. So the amount of investment required to purchase A is relatively small, and B is somewhat larger, and the asset that requires the largest initial investment is D. And then note that these internal rates of return fall, A being the one with the highest internal rate of return, then B, then C, then D, then E. And this follows the same pattern that we had from that single-period choice optimal pace problem, where you order your benefits from highest initial benefit to lowest initial benefit, and that's what we've done here.

And the other thing I've added in is a red line, and that red line indicates the minimum acceptable rate of return. And, it is ordered the same way that we had at our single period choice. It is ordered from lowest incremental cost to highest incremental cost — it just so happens that they're exactly the same. And we can use this diagram to replicate the results that we have from the internal rate of return criteria when everything is an investment, and everything here IS an investment. The investment criteria for internal rate of return is you buy the asset if the internal rate of return (the height of this bar here) is greater than or equal to the minimum acceptable rate of return (the height of the red line). So clearly asset A has a high internal rate of return relative to minimum acceptable — you should buy it. Same thing for asset B, it has a high internal rate of return relative to the minimum acceptable — you can buy it. And that's true for all the assets C, D, but not E, E has a low internal rate of return relative to minimum acceptable — it should not be purchased.

So that's the tool that we have when we have our usual environment of unconstrained choice with a single source of funds with the minimum acceptable rate of return constant, for all [unintelligible].

I've altered the diagram just a little bit. I've removed this big section of line that we had here which represented that minimum acceptable rate of return extending out forever. What I said is that this red line here represents a certain limited amount of retained earnings — and remember retained earnings have a low minimum acceptable rate of return — and they run out just as you are finishing purchasing of asset C, and then after that this blue line right here represents funds you have available in order to borrow from somebody else — these are loan funds. And I've ordered these incremental costs — the sources of your funds — from lowest incremental cost here, to highest incremental cost here — so we can follow the same rule that we had for single-period choice as long as your incremental benefits (which are the internal rate of return) are higher than your incremental costs (the minimum acceptable rate of return) you're supposed to buy it. So in this situation here, you'd definitely purchase asset A, you'd definitely purchase asset B, you'd definitely purchase asset C, just see D is no longer feasible because it's incremental costs (indicated by the blue line right up here, that higher loan rate) is higher than your internal rate of return (that's your incremental benefit).

Now, we could go ahead and alter this ever so slightly: we could have made it so that this blue line extended all the way back to B. You see that in that case, we could actually fund asset A from retained earnings, asset B from retained earnings, and if we extended this line back, saying that we ran out of our retained earnings just as we're going to the B border. What you would see is that you could actually buy asset C with the loan, but not get asset D, because it wouldn't make sense. So, all we're doing here is showing you that you can maximize your net benefits by following this same rule that you saw before, as long as your incremental benefits are greater than your incremental costs, you can go ahead and buy. And I've purposefully put that little break between the retainer and [?? this here] loan right on one of those borders where you have fully purchased one of the assets with the retained earnings before you switch to the loan.

Now I've changed this problem just a little bit at this point and I've given you a little extra retained earnings — and so what I've done is I've extended this red line out here, so you have enough cash in order to cover asset A, you have enough cash to cover asset B, you have enough cash to cover asset C, but partway through trying to purchase D you run out of retained earnings and have to shift up to this loan right here. Now, clearly E is never going to be purchased, but let's talk about this asset D that you have right there. Because how you handle your choice about purchasing asset D depends upon what kind of asset it is. Asset A can clearly be purchased, since its incremental benefits are greater than its incremental cost. Asset B can be clearly purchased, so can asset C, but asset D is one of those cases where it depends. Now, if asset D is a divisible asset — which means it makes sense in order to, say, cut in half, or cut it into a third — when, what you can do is you can think about it not as "just D," but, say, part of D, and another part of D. An example of a divisible asset could be if you're talking about some loading docks, you can talk about a 20-bay loading dock. You can also picture seeing having a ten-bay loading dock, or a five-bay loading dock. So, something that you can cut into chunks. If asset D is something like, say, a ship, you can't cut a ship in half, it just doesn't work that way. Or a car, having half a car doesn't do anything, that would be an indivisible asset. But if it's divisible, you can picture taking asset D and just dividing it, it's two chunks, and that's what I'm doing right here. You can think of those two chunks simply as being "part D-1," "part D-2". What you can do is you can think about the purchase of part D-1 and part D-2 separately. Part D-1 here — which is just this narrow sequence, this narrowness indicates your initial investment — has an incremental cost of only this red line here (your retained earning rate), but an incremental benefit equal to that internal rate of return on the whole asset. Part D-2, however, has an incremental cost equal to this blue line, which is above your internal rate of return. So, D-1 should be purchase, while D-2 should not. And that's how you handle these kinds of asset choices when you have divisible assets.

For indivisible assets, it becomes somewhat complicated because you have to figure out what exactly the incremental cost actually means. So, really what you're looking at is what are the cost of funds for that whole asset. And if you think of it as having part of your money come from retained earnings and part of your money coming from loans, you can see that you're actually trying to find a blended average of those minimum acceptable rates of return. So, if you were buying 1/3 of this asset with retained earnings and 2/3 with a loan, you could go ahead and say, "well, it's 1/3 times the retained earning rate, plus 2/3 times the loan rate" and that would give you the blended minimum acceptable rate of return that you could compare to the internal rate of return. And as long as that internal rate of return was greater than minimum acceptable, you'd go ahead and buy this asset.